Problem: In a particular game, a player can earn either 3 points or 5 points on each turn. If Capri has earned a total of 18 points, what is the fewest number of turns she could have taken?
Solution: Let's say that Capri earned 3 points on $a$ turns and 5 points on $b$ turns. We want to minimize $a+b$, the total number of turns. We also know that Capri scored a total of 18 points on her turns so we get $$3a+5b=18.$$ This is only possible when $a=6$ and $b=0$ or when $a=1$ and $b=3$. which produce 6 and 4 total turns respectively. Therefore, the fewest number of turns Capri could have taken is $\boxed{4}.$